Well-posedness of the boundary value problem for parabolic equations in difference analogues of spaces of smooth functions

DOI10.1155/2007/90815zbMath1152.65089OpenAlexW2038504092MaRDI QIDQ936190

Allaberen Ashyralyev

Publication date: 13 August 2008

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/54905

zbMATH Keywords

well-posednessBanach spacenonlocal boundary value problemstrongly positive operatorcoercive stabilityimplicit difference schemefractional spacecoercive inequality

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solutions to equations with linear operators (65J10) Linear differential equations in abstract spaces (34G10) Finite difference and finite volume methods for ordinary differential equations (65L12)

Cites Work

• Approximation of abstract differential equations
• Finite-difference methods for solution of nonlocal boundary value problems
• Stability of difference schemes for hyperbolic-parabolic equations
• Nonlocal boundary-value problems for abstract parabolic equations: well-posedness in Bochner spaces
• Nonlinear parabolic equations with regularized derivatives
• Well-posedness of parabolic difference equations. Transl. from the Russian by A. Iacob
• Stability of a nonlocal two-dimensional finite-difference problem
• Coercive solvability of the nonlocal boundary value problem for parabolic differential equations
• Estimates of variable stepsize Runge-Kutta methods for sectorial evolution equations with nonsmooth data
• On the stability of a nonlocal finite-difference boundary value problem
• On well-posedness of the nonlocal boundary value problem for parabolic difference equations
• On the numerical solution of the diffusion equation with a nonlocal boundary condition
• Coercive boundary value problems for regular degenerate differential-operator equations
• New difference schemes for partial differential equations.
• The stability of rational approximations of analytic semigroups
• Linearly-implicit, approximate factorization, exponential methods for multidimensional reaction-diffusion equations
• Maximal regular boundary value problems in Banach-valued weighted space
• FDM for multi-dimensional nonlinear coupled system of parabolic and hyperbolic equations
• Time-nonlocal problems for Schrödinger type equations. I: Problems in abstract spaces
• Exponentially Convergent Parallel Discretization Methods for the First Order Evolution Equations
• A Galerkin Procedure for the Diffusion Equation Subject to the Specification of Mass
• Well-posed solvability of the Cauchy problem for difference equations of parabolic type
• H2,r-convergent approximation schemes to the Navier-Stokes equations
• Algorithms without accuracy saturation for evolution equations in Hilbert and Banach spaces
• ON WELL-POSEDNESS OF DIFFERENCE SCHEMES FOR ABSTRACT PARABOLIC EQUATIONS INL^P([0,T;E) SPACES]
• Exponentially Convergent Algorithms for the Operator Exponential with Applications to Inhomogeneous Problems in Banach Spaces
• Analytic semigroups and optimal regularity in parabolic problems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Well-posedness of the boundary value problem for parabolic equations in difference analogues of spaces of smooth functions